“People are so horrified,” says Sunny Mindel, the publicly scowling yet wickedly funny woman who has spent four years at Rudy Giuliani’s side as spokeswoman and then communications director.

“They think I should be smoking nonfilter cigarettes, not these fouffy menthol ones,” the 40-something Mindel says with a hint of a smoker’s cough.

That Sunny should be talking about something as personal as what she puts in her mouth is unusual. Two years ago, Mindel was promoted to run the mayor’s communications department, a job she inherited from Cristyne Lategano, whose private life was made into public fodder by Giuliani’s bitter estranged wife, Donna Hanover.

Sunny became so private, she declined a ceremony marking her promotion. But now that she’s moving out of City Hall, details can be told. Sunny, who is divorced without children, has for a year been involved with lawyer John Kaufmann of the firm Winston and Strawn.

Also, Mindel is taking a job in Giuliani’s new consulting firm. This the mayor told me himself – Sunny won’t discuss it.

Before working on Giuliani’s re-election campaign, Mindel was a freelance reporter for WNYC. Working for Giuliani was an epiphany – her admiration turned to loyalty so fierce, the job became all-consuming.

During the nastiest days of Giuliani’s divorce, Mindel had the task of representing him in that mess. She hated it.

Her relations with the press have at times seemed bitter. Like Giuliani, she doesn’t care much what people think of her.

But since Sept. 11, when she was trapped with the mayor inside 75 Barclay St. as the first tower fell, her media relations have softened.

“The press corps performed so valiantly and courageously on Sept. 11. Their lives were in jeopardy, and yet they got up the next day and went to work.”

Others who performed valiantly include press secretary Matt Higgins and spokeswoman Lynn Rasic, who would have been killed on the 11th had they not abandoned the sound box they were setting up for a press conference at ground zero.

And deputy press secretary Peter Fenty and spokesman Sid Dinsay, and Warner Johnson of the Department of Citywide Services.

The end of the Giuliani administration allows Sunny to engage in her new favorite hobby – “sleeping.”